Shortest Distance Between Lines (Jee Mains)

3D Line Equations and Skew

Hard

Shortest Distance Between Lines

The sum of all values of α, for which the shortest distance between the lines
$\frac{{x + 1}}{\alpha } = \frac{{y - 2}}{{ - 1}} = \frac{{z - 4}}{{ - \alpha }}$ and $\frac{x}{\alpha } = \frac{{y - 1}}{2} = \frac{{z - 1}}{{2\alpha }}$ is $\sqrt 2$ , is

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